If the four-sided spinner that I spoke about in the last blog is used again and again you would expect the convergence that I also spoke about. What does it mean if there is no convergence? If the spinner lands on d 20 times in the first 50 spins then this gives it a relative fr of 20/50= 0.4 You would expect it to have one chance in four and the relative frequency should be

After 60 spins there is a relative frequency of 0.45. How do you work out the actual number of times it has landed on d. You multiply 60 by 0.45 and you have the answer 27. So just looking at the relative frequency it should be 0.2 The more times that you spin the spinner the more chance of achieving the relative frequency of 0.2 but it just isn't happening. There is no convergence so there must be bias. The spinner falls more on d than the other letters. Think of the design as if it were a matchstick piercing a small square piece of paper and each side is labelled a b c and d. When it stops spinning the lowest side wins so it could be that there is some blu-tack on the d.

That sums it up.

## Sunday, 26 April 2009

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